Self-organization of vortex-length distribution in quantum turbulence: An approach based on the Barabási-Albert model

The energy spectrum of decaying quantum turbulence at $T=0$ obeys Kolmogorov's law. In addition to this, recent studies revealed that the vortex-length distribution (VLD), meaning the size distribution of the vortices, in decaying Kolmogorov quantum turbulence also obeys a power law. This power-law VLD suggests that the decaying turbulence has scale-free structure in real space. Unfortunately, however, there has been no practical study that answers the following important question: why can quantum turbulence acquire a scale-free VLD? We propose here a model to study the origin of the power law of the VLD from a generic point of view. The nature of quantized vortices allows one to describe the decay of quantum turbulence with a simple model that is similar to the Barab\'asi-Albert model, which explains the scale-invariance structure of large networks. We show here that such a model can reproduce the power law of the VLD well.